Help with introducing some equational theories

[Shrey Mukund]

Dear All, 

I am trying to work on protocols to verify their security, and I am very new to Tamarin .However, for one protocol, I am trying to introduce an equational Theory of the form: 

F(a,b, 'g'^c, 'g'^d, e,f) = F(a,b, 'g'^e, 'g'^f, c,d) 

I modelled it as follows: 


However, I am facing the following error. 

After trying different things, I discovered that the Diffie-Hellman 'g'^c operations are not working well with the theory. 
The following are some equational theories used, and I have received an error. 

Maybe I am missing something. I am not sure. Could anyone please suggest a better way to model this? 
 

If not, I would have to introduce exponentiation operators, which might make the model too abstract and impossible to find attacks if they exist.

Thank you